Topic 7

Modern Physics

From the atom to the Standard Model, modern physics explores the deep structure of matter, the origin of mass, nuclear energy, and the questions that define the frontiers of 21st-century physics.

Atomic models & the Bohr model
Nuclear physics & radioactivity
Particle physics & the Standard Model
Where does mass come from?
Open questions & frontiers

1. Atomic Models & the Bohr Model

By the early 1900s, experiments revealed that atoms were mostly empty space with a tiny, dense nucleus. Rutherford's gold-foil experiment (1911) fired alpha particles at thin gold — most sailed through, but a few bounced straight back, proving the nucleus was both dense and small. But why don't orbiting electrons spiral into the nucleus, radiating away energy as Maxwell's equations demand?

Niels Bohr (1913) proposed a radical fix: only certain orbits are allowed, and they don't radiate. An electron can jump between orbit $n$ and $n'$, emitting or absorbing a photon with energy equal to the level difference:

$$\boxed{E_n = -\frac{13.6\,\text{eV}}{n^2},\qquad \Delta E = hf = \frac{hc}{\lambda}}$$

This explained the atomic emission spectra of hydrogen perfectly — only photons with specific energies (corresponding to allowed transitions) are emitted. Bohr's model was a stepping stone: it merged classical orbits with quantum leaps, but the full theory (quantum mechanics, covered in the previous section) replaced orbits with probability clouds — atomic orbitals.

Hydrogen energy levels (Bohr model, 1913). Arrows show transitions producing the Lyman (UV), Balmer (visible), and Paschen (infrared) spectral series.

2. Nuclear Physics & Radioactivity

The nucleus contains nucleons (protons and neutrons) at densities so extreme that a teaspoon of nuclear matter weighs ~10¹⁹ kg. But nuclei are held together by a subtle balance. Radioactive decay transforms one element into another:

$$N(t) = N_0\,e^{-\lambda t},\qquad T_{1/2} = \frac{\ln 2}{\lambda}$$

The half-life is constant — independent of chemical environment, pressure, or temperature. Carbon-14 dating (half-life 5,730 years) lets us date organic artifacts up to ~50,000 years old. The three natural decay modes are:

Alpha ($\alpha$): emits $^4_2\text{He}$; heavy, low penetration.
Beta ($\beta$): emits an electron (or positron) and a neutrino; medium penetration.
Gamma ($\gamma$): emits a high-energy photon; high penetration (requires dense shielding).

Nuclear binding energy — The energy that holds nuclei together, from Einstein's $E=mc^2$. When a heavy nucleus splits (fission) or two light nuclei fuse (fusion), mass is converted to energy. The mass defect $\Delta E = \Delta m\,c^2$ powers the Sun, nuclear reactors, and stars.

$$\Delta E = \Delta m\,c^2$$

3. The Standard Model of Particle Physics

Everything in the universe (as far as we know) is made of elementary particles, organized in the Standard Model. There are two families of matter and the forces that act on them:

Category	Particles	Mass
Quarks (matter)	up, down, charm, strange, top, bottom	2–173 GeV/c²
Leptons (matter)	electron, muon, tau, + 3 neutrinos	0–178 MeV/c²
Force carriers	photon (γ), W/Z bosons, gluon (g)	0 (γ,g), 80–91 GeV
Higgs	one scalar boson	125 GeV/c²

The three light quarks (up, down, strange) combine to form protons, neutrons, pions, and the zoo of hadrons. The Higgs boson (discovered 2012) confirmed the mechanism by which the W and Z bosons — and through them, all elementary particles — acquire mass. But the Higgs mechanism explains only ~1% of the proton's mass; most of it comes from the strong interaction binding energy via $E = mc^2$.

What the Standard Model doesn't include. Gravity (described by general relativity) is not yet quantized. Dark matter, dark energy, and neutrino masses are observed but unexplained. The Standard Model is a symptom of a deeper theory — string theory, loop quantum gravity, or something we haven't imagined — that unifies all four forces.

4. Where Does Mass Come From?

Most of the mass of your body didn't come from the Higgs. A proton weighs ~938 MeV/c², but its two up quarks and one down quark sum to only ~5 MeV/c². The other 99% comes from gluonic binding energy — the kinetic and potential energy of quarks and gluons trapped by the strong force. This is a direct consequence of $E = mc^2$: energy has mass.

$$\boxed{E = mc^2}$$

The Higgs field gives mass to the elementary particles (W, Z, electrons) via the Higgs mechanism. But the mass of protons and neutrons — and hence of planets, people, and pianos — arises from the strong force. We are, quite literally, made of stardust and binding energy.

5. Open Questions & Frontiers

Modern physics has answered profound questions, but deeper ones remain:

Question	Why it matters
Quantum gravity	Reconcile general relativity (smooth spacetime) with quantum mechanics (discrete, probabilistic).
Dark matter	85% of matter in the universe is invisible — inferred from galaxy rotation curves but never directly detected.
Dark energy	The universe's expansion is accelerating, driven by energy with negative pressure.
Unification	All forces were one at the Big Bang; can we find a single theory of everything?
Measurement problem	Why do superpositions "collapse" to definite outcomes? Is consciousness involved?

The Standard Model is incomplete, not wrong. Every prediction tested — from the magnetic moment of the electron to the Higgs boson mass — matches experiment. But it contains ~20 free parameters (masses of particles, coupling strengths) that the Standard Model itself cannot predict. A deeper theory should explain why the masses and forces have the values they do. String theory, with its extra dimensions, is one ambitious attempt; others include loop quantum gravity and the search for physics beyond the Standard Model at the Large Hadron Collider.

Key Takeaways

Atoms have tiny, dense nuclei surrounded by electron orbitals — Bohr's quantized model explained hydrogen's spectrum.
Radioactive decay follows exponential laws with constant half-lives; nuclear binding energy ($E=\Delta mc^2$) powers stars and reactors.
The Standard Model organizes particles into quarks, leptons, and force carriers — with the Higgs giving mass to elementary particles.
99% of visible mass comes from strong-force binding energy, not the Higgs — we are made of $E=mc^2$.
Frontiers remain: dark matter, dark energy, quantum gravity, and a unified theory.

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